91Ó°ÊÓ

The heating element is part of an electric heating appliance in which electric energy is transformed into heat.

Heating element power $P=4.1kW\left(\frac{{10}^{3}W}{1kW}\right)=4.1×{10}^{3}W$

Connected line voltage = 240 V

(a)

The current is given as,

$I=\frac{P}{V}$…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦.(1)

Substitute the values of P and V in equation (1) to get the current,

$$\begin{gathered} =\frac{4.1×{10}^{3}W}{240V} \\ =17.08A \end{gathered}$$

Thus, the current in the heating element is which is safe for 12-gauge wire.

(b)

The power dissipated is given as,

$P=\frac{V^2}{R}$ (2)

Substitute all the values in equation (2) which gives resistance,

$$\begin{gathered} R=\frac{{\left(240V\right)}^2}{4.1×{10}^{3}W} \\ =14.1\mathrm{Î\copyright } \end{gathered}$$

Thus, the resistance of the dryer’s heating element at its operating temperature is $14.1\mathrm{Î\copyright }$

(c)

The dryer costs 11 cents for the energy of 1 kWh.energy consumed by the dryer is,

$$\begin{gathered} E=P×t \\ E=4.1kW×1h \\ E=4.1kWh \end{gathered}$$E=pt.=(4.1kW) (1h) =4.1kWh

The cost of operating the dryer for 1 h can be calculated as,

$$\begin{gathered} Operatingcost=41KWh×11Cent/KWh \\ =451Cent \end{gathered}$$

Thus, the cost per hour to operate the dryer is 45.1 Cents